Question

The surface area of a solid hemispherical object is 165 ft${}^2$. What is the diameter of the hemisphere ?

• A. 8.370 ft
• B. 8.170 ft
• C. 7.370 ft
• D. 9.370 ft

Answer 1

The correct option is A 8.370 ft

Given:
Surface Area= 165 ft${}^2$
Surface area of a hemisphere = $3\pi r^2$
$\Rightarrow 165=3\times 3.14\times r^2$
$\Rightarrow 165=9.42r^2$
Divide both sides by 9.42 to get,
$\Rightarrow 17.516=r^2$
$r=\sqrt{17.516}$
= 4.185 ft
Hence the radius is 4.185 ft but the diameter is twice the radius.
So, the diameter of the hemisphere is 8.370 ft.
Hence, the correct answer is option (a)